Electrodynamic method

ABSTRACT

An electrodynamic method includes providing an electrodynamic structure with a periphery, providing power, collecting electrons, and emitting electrons. The emitting electrons and the collecting electrons utilizes at least 20% of the periphery of the electrodynamic structure. The method includes conducting current to provide at least one of electrodynamic propulsion and power generation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This Patent Application is a Divisional of and claims priority toco-pending U.S. patent application Ser. No. 11/372,508, filed on Mar.10, 2006, which is incorporated herein by reference.

BACKGROUND

The potential use of long electric conductors in space in a form ofelectrodynamic tethers was discovered in early 80's. Electrodynamictethers in space have attracted a lot of attention in recent years. Manyresearchers have contributed to the theory of their behavior in orbit.Some flight experiments have provided data on the interaction betweenthe electrodynamic tethers and the geomagnetic field and ionosphere.

Typically, an electrodynamic tether is a long electrical conductor thatcan be used to generate power and/or propulsion as the tether orbits acelestial body with a magnetic field. Flight experiments have provideddata on the interaction between electrodynamic tethers and thegeomagnetic field and ionosphere of the Earth.

In 1993, the Plasma Motor Generator (PMG) experiment was performed on aDelta rocket with a primary goal of testing power generation and thrustby means of an electrodynamic tether. In the PMG experiment, a 500 meter(m) long electrodynamic tether was deployed into the ionosphere. Thetether included a conducting wire with hollow cathodes at each end. Anelectric current was produced in the tether, demonstrating the potentialof this technique to generate power and propulsion that could be used bysatellites or space stations in low Earth orbit (LEO). The PMG missionwas an example of a propulsion system for space transportation that didnot utilize propellant, but rather achieved propulsion by convertingorbital energy into electrical energy (deorbit) or electrical energyinto orbital energy (orbit boosting).

Two Tethered Satellite System (TSS) missions were flown in 1992 and1996. The TSS included a satellite, a conducting tether, and a tetherdeployment/retrieval system flown on the Space Shuttle. Objectives ofthe TSS missions were to understand the electro-magnetic interactionbetween the tether system and the ambient space plasma, investigate itsdynamics, and demonstrate current collection from the ionosphere tofurther develop tether capabilities for future tether applications onthe Space Shuttle and Space Station. In the TSS-1 mission of 1992, thetether was only partially deployed and the mission was aborted.

The TSS-1R mission of 1996 was a re-flight of the TSS-1 mission. Thetether was deployed to the length of 19.7 km when it was severed by anelectrical arc. Nevertheless, it was a significant mission for tetheredsatellites because it showed that electrodynamic tethers were moreefficient than theoretically predicted, providing valuable data onelectrical performance of the system. Power generation of severalkilowatts was demonstrated.

“Tethers in Space Handbook,” Second Edition, NASA Office of SpaceFlight, NASA Headquarters, Washington, D.C., 1989, edited by P. A. Penzoand P. W. Ammann, provides summaries of various applications andfeatures of electrodynamic tethers, including methods to change orbitalelements with electrodynamic tether propulsion and methods to controlattitude dynamics of tethers.

Typically, electrodynamic tethers are very long and operate at highvoltages. The electrodynamic tethers run the risk of arcing as in theTSS-1R mission. Also, the electrodynamic tethers are susceptible todamage from meteors and/or debris due to the length of the tethers. Inaddition, electrodynamic tethers are difficult to scale up to move heavypayloads.

For these and other reasons, there is a need for the present invention.

SUMMARY

One embodiment provides an electrodynamic method including providing anelectrodynamic structure with a periphery, providing power, collectingelectrons, and emitting electrons. The emitting electrons and thecollecting electrons utilizes at least 20% of the periphery of theelectrodynamic structure. The method includes conducting current toprovide at least one of electrodynamic propulsion and power generation.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the present invention and are incorporated in andconstitute a part of this specification. The drawings illustrate theembodiments of the present invention and together with the descriptionserve to explain the principles of the invention. Other embodiments ofthe present invention and many of the intended advantages of the presentinvention will be readily appreciated as they become better understoodby reference to the following detailed description. The elements of thedrawings are not necessarily to scale relative to each other. Likereference numerals designate corresponding similar parts.

FIG. 1 is a diagram illustrating one embodiment of an electrodynamicstructure according to the present invention.

FIG. 2 is a diagram illustrating the flow of electrons in atwo-dimensional, planar electrodynamic structure.

FIG. 3 is a diagram illustrating one embodiment of electrical componentsin a portion of a periphery area.

FIG. 4 is a diagram illustrating one embodiment of an open net-likecollector structure.

FIG. 5 is a diagram illustrating one embodiment of a circular,two-dimensional, planar electrodynamic structure that includes a mesh ofconductors.

FIG. 6 is a diagram illustrating one embodiment of a hexagonal,two-dimensional, planar electrodynamic structure that includes atriangular mesh of conductors.

FIG. 7 is a diagram illustrating one embodiment of a rectangular,two-dimensional, planar electrodynamic structure that includes a mesh ofconductors.

FIG. 8 is a diagram illustrating one embodiment of a rectangular,two-dimensional, planar electrodynamic structure that has only partialperiphery utilization for electron collection and electron emission.

FIG. 9 is a diagram illustrating one embodiment of a cylindrical,three-dimensional electrodynamic structure.

FIG. 10 is a diagram illustrating one embodiment of a curved,half-elliptical, three-dimensional electrodynamic structure.

FIG. 11 is a diagram illustrating one embodiment of an enclosed,three-dimensional electrodynamic structure.

DETAILED DESCRIPTION

In the following Detailed Description, reference is made to theaccompanying drawings, which form a part hereof, and in which is shownby way of illustration specific embodiments in which the invention maybe practiced. In this regard, directional terminology, such as “top,”“bottom,” “upper,” “lower,” “front,” “back,” etc., is used withreference to the orientation of the Figure(s) being described. Becausecomponents of embodiments of the present invention can be positioned ina number of different orientations, the directional terminology is usedfor purposes of illustration and is in no way limiting. It is to beunderstood that other embodiments may be utilized and structural orlogical changes may be made without departing from the scope of thepresent invention. The following detailed description, therefore, is notto be taken in a limiting sense, and the scope of the present inventionis defined by the appended claims.

FIG. 1 is a diagram illustrating one embodiment of an electrodynamicstructure 20 according to the present invention. Electrodynamicstructure 20 is configured to generate power and/or propulsion as itorbits a celestial body having a magnetic field. In one aspect,electrodynamic structure 20 is an electrodynamic sail. In otherembodiments, electrodynamic structure 20 can be part of any suitablesystem, such as a space station.

Electrodynamic structure 20 is substantially a circular,two-dimensional, planar electrodynamic structure that includes aperiphery area 22 and supports 26. As illustrated, electrodynamicstructure 20 is coupled to a payload 24. Periphery area 22 is situatedat the periphery of electrodynamic structure 20 and has width W. Payload24 is disposed in the center of electrodynamic structure 20 and ismechanically coupled to periphery area 22 via supports 26. An interiorarea 25 is defined between an interior edge of periphery area 22 andpayload 24. In one embodiment, interior area 25 includes open gaps(i.e., gaps that do not contain components or material) between each ofthe supports 26.

In some embodiments, some or all parts and components are mounted on asubstrate, such as a plastic film, to provide mechanical support. Insome embodiments, a portion or all of periphery area 22 is covered witha substrate. In some embodiments, a portion or all of interior area 25is covered with a substrate. In one embodiment, the substrate is areflective film.

In the embodiment illustrated in FIG. 1, periphery area 22 includeselectron collectors 28, electron emitters 30, solar arrays 32, and oneor more controllers 34. As illustrated, electron collectors 28 andelectron emitters 30 are situated at an outer rim of periphery area 22.As illustrated, solar arrays 32 are situated at an interior rim ofperiphery area 22.

In embodiments of two- or three-dimensional electrodynamic structures,electron collectors, electron emitters, solar arrays, and controllerscan be disposed in the periphery area, such as periphery area 22.Additionally, in embodiments of two- or three-dimensional electrodynamicstructures, electron collectors, solar arrays, and controllers can bedisposed in the interior area, such as interior area 25.

Electron collectors 28, electron emitters 30, solar arrays 32, andcontrollers 34 are electrically coupled via conductive paths formed withswitches and conductors. The conductive paths are not shown in FIG. 1for clarity, but one embodiment of a portion of a periphery areaincluding conductive paths formed with switches and conductors isillustrated in FIG. 3 and discussed below. In one embodiment, electroncollectors 28 are electrically coupled to each other via conductivepaths formed with switches and conductors. In one embodiment, electronemitters 30 are electrically coupled to each other via conductive pathsformed with switches and conductors. In one embodiment, solar arrays 32are electrically coupled to each other via conductive paths formed withswitches and conductors. In one embodiment, conductive paths includeconductors that include insulated strips of aluminum foil.

Supports 26 are members that mechanically couple payload 24 to peripheryarea 22. In one embodiment, supports 26 are non-rigid supports. In oneembodiment, supports 26 are mechanically stiffened supports. In oneembodiment, supports 26 are conductive and payload 24 and electricalcomponents in periphery area 22 are electrically coupled via theconductive supports 26.

In embodiments of two- or three-dimensional electrodynamic structures,payloads, such as payload 24, can be any suitable payload, such as asatellite that orbits the Earth, an inter-planetary satellite, or asatellite that orbits any suitable celestial body. In one embodiment,electrical components in the periphery area, such as periphery area 22,are electrically coupled to the payload (e.g., payload 24) via supports(e.g., support 26) and the payload receives power from electricalcomponents in the periphery area. In one embodiment, the payloadincludes one or more controllers that control operation of theelectrodynamic structure (e.g., electrodynamic structure 20).

The electron collectors, such as electron collectors 28, describedherein are defined to collect electrons from the ambient plasma. In oneembodiment, the electron collectors are bare aluminum coated surfaces.In other embodiments, the electron collectors can be any suitable typeof electron collectors.

The electron collectors can cover not only a relatively narrow bandaround the periphery (e.g., periphery area 22) of the electrodynamicstructure, but also much wider areas, reaching into the interior (e.g.,interior area 25) of the electrodynamic structure. In one embodiment,the entire surface of the electrodynamic structure is employed forelectron collection.

The electron emitters, such as electron emitters 30, described hereinare defined to emit electrons into the ambient plasma. In oneembodiment, the electron emitters are field emitter array cathodes(FEACs). In other embodiments, the electron emitters can be any suitabletype of electron emitters.

The solar arrays, such as solar arrays 32, described herein are definedto absorb solar energy, and provide power in the form of electricity. Inone aspect, solar arrays are one type of power system. In one aspect,solar arrays are solar energy collection devices. In one embodiment,solar arrays are thin-film solar arrays. In embodiments of two- orthree-dimensional electrodynamic structures, any suitable power systemcan be used to generate power and electricity.

One or more controllers, such as controller 34, control operation ofembodiments of electrodynamic structures (e.g., electrodynamic structure20) via the switches and conductors in the conductive paths. FIG. 2 is adiagram illustrating the flow of electrons in a two-dimensional, planarelectrodynamic structure, such as electrodynamic structure 20. At 50,electron collectors (e.g., collectors 28) on one side of theelectrodynamic structure are controlled with one or more controllers tocollect electrons from ambient plasma. Under the control of one or morecontrollers, the collected electrons are driven to electron emitters(e.g., emitters 30) on the opposite side of the electrodynamic structurevia conductors in the conductive paths. The collected electrons aredriven using power generated via the power system (e.g., solar arrays32). In addition, the motion through the ambient magnetic field producesan electro-motive force (EMF) in the conductors of the conductive paths,which can also be used to drive electrons to the opposite side of theelectrodynamic structure in the direction of the EMF. At 52, electronemitters (e.g., emitters 30) on the opposite side of the electrodynamicstructure are controlled by one ore more controllers to emit electronsinto the ambient plasma. The currents flowing through the conductors ofthe conductive paths between the electron collectors and the electronemitters interact with the ambient magnetic field to produce distributedAmpere forces, which can be employed to change the orbit and theorientation of the electrodynamic structure.

In one embodiment, the area of electron collection at 50 and the area ofelectron emission at 52 are determined dynamically, as theelectrodynamic structure moves including as the electrodynamic structurerotates, in the magnetic field of the celestial body and as theelectrodynamic structure moves including as the electrodynamic structurerotates around its center of mass. In the area of electron collection at50, electron emitters remain inactive and in the electron emission areaat 52, electron collectors remain inactive. As the electrodynamicstructure moves, electron collectors and electron emitters are turned on(selected) and turned off (deselected) at switching line 54 via one ormore controllers to maintain one side as the area of electron collectionat 50 and the other side as the area of electron emission at 52.

Conductors employed in embodiments of two- or three-dimensionalelectrodynamic structures can operate bi-directionally in the sense thatthe electrical current can flow either in the direction of the EMFinduced in the conductor, or in the reverse direction, depending on theconductor orientation with respect to the magnetic field, mission goals,available power, and other system parameters. The reverse current isdriven by available power sources, such as solar arrays 32. If thecurrent is reversed, electron collection and electron emission locationsare reversed. Electron collection and emission occurs at multiplelocations at the same time, to allow better utilization of thrust andpower generation capabilities and to better control dynamics andoptimize orbital maneuvering.

Electrodynamic structure 20 is substantially a two-dimensional, planarelectrodynamic structure having a circular shape. Embodiments oftwo-dimensional electrodynamic structures can be any suitable physicalshape, such as, elliptical (e.g., circular, elongated elliptical) orpolygonal, (e.g., rectangular, square, hexagonal).

Embodiments of two-dimensional electrodynamic structures (e.g.,electrodynamic structure 20) can be spin stabilized, wherein the spinaxis is normal to the plane of the figure, such as FIG. 1. Embodimentsof electrodynamic structures can spin at angular rates of 2 to 36 timesthe orbital rate. In each application, the spin rate is chosen based onperformance and design trade-offs. In one embodiment, the electrodynamicstructure spins at an angular rate that is substantially 6 to 8 timesthe orbital rate.

Embodiments of electrodynamic structures (e.g., electrodynamic structure20) can adjust spin axis, spin rate, and/or spin phase by varyingdirection, duration, amount, and/or path-length of currents flowingthrough the conductors. The orientation of the spin axis with respect tothe orbital plane is chosen as best suited for a particular mission. Forexample, the spin axis can be pointed toward the Sun to maximize solarenergy collection. Throughout the mission, the evolution of the spinaxis orientation, the average spin rate, and the spin phase arecontrolled by modulations of the electrodynamic torques produced byvariations in the electric current through the conductive paths. Thespin-control current variations can be chosen to optimize theperformance of the electrodynamic structure, while maintainingstability.

Due to the spinning of embodiments of two-dimensional electrodynamicstructures, the EMF induced in the conductors of the conductive pathschanges direction during every revolution. To optimize variations inorbital elements and/or to optimize power generation, switches arecontrolled to drive electrons in a different direction during eachrevolution of the electrodynamic structure. As the electrodynamicstructure spins, the switches are controlled to switch from electroncollection on one side of the electrodynamic structure to electroncollection on the other side of the electrodynamic structure and toswitch from electron emission on the other side of the electrodynamicstructure to electron emission on the one side of the electrodynamicstructure.

Since, the respective orientations of embodiments of spinningtwo-dimensional electrodynamic structures to the magnetic field arecontinuously changing and the currents in the conductors change with therotation of the electrodynamic structure, the long-term evolution of theorbital and spin parameters is defined by a cumulative effect of theAmpere forces over periods of time longer or much longer than the spinperiod. Short-term oscillations of the dynamic and electrical parametersof the system, with periods shorter or much shorter than the spinperiod, are superimposed on the long-term evolution. The overallperformance of electrodynamic structures can be estimated by averagingover a period of many orbits, which takes into consideration severalgroups of factors, including factors that change with the spin period,factors that change with the orbital period, and factors that changewith the magnetic field rotation of the celestial body.

The performance level of a substantially two-dimensional electrodynamic,planar structure (e.g., electrodynamic structure 20) can be estimatedvia Equation I.

F/M=K*U*(I/M)*B*(S/P)  Equation I

wherein F/M is the average total propulsion force of the electrodynamicstructure per unit mass of the electrodynamic structure;

-   U is the fraction of the periphery of the electrodynamic structure    utilized for electron collection and emission;-   (I/M) is the average total current collected and emitted per unit    mass of the electrodynamic structure;-   B is the induction of the magnetic field of the celestial body;-   P is the value of a structure perimeter, where the periphery of the    electrodynamic structure defines the structure perimeter;-   S is the area enclosed by the structure perimeter; and-   K is a dimensionless coefficient based on the electrodynamic    structure implementation.

Parameters in Equation I related to two-dimensional electrodynamicstructures, such as electrodynamic structure 20, can be maximized tooptimize the performance level of the electrodynamic structure. Suchparameters include periphery utilization for electron collection andemission U, area to perimeter ratio (S/P), and electric currentproduction per unit mass of the electrodynamic structure (I/M). In manyembodiments, parameter K is close to 2. The magnetic induction B doesnot depend on characteristics of the electrodynamic structure.

In some embodiments, to maximize U, the entire periphery of theelectrodynamic structure (e.g., electrodynamic structure 20) is linedwith electron collectors (e.g., collectors 28) and electron emitters(e.g., emitters 30), as illustrated in FIG. 1. This yields a utilizationfactor of U=1 or 100%. If half of the periphery of the electrodynamicstructure includes electron collectors and electron emitters and theother half is empty, U=½ or 50%. It is overly inefficient for theelectrodynamic structure to have periphery utilization U of less than ⅕or 20%.

The area to perimeter parameter (S/P) is maximized if the electrodynamicstructure is circular such as electrodynamic structure 20. Other shapes,provide smaller area to perimeter ratios (S/P). Square or hexagonalshapes provide smaller but comparable (S/P) ratios, while elongatedshapes, such as elongated elliptical shapes and elongated rectangularshapes have substantially lower (S/P) ratios. It is overly inefficientfor the electrodynamic structure to have an area to perimeter ratio(S/P) less than ¼ or 25% of the ratio for a circle with the sameperimeter.

The electric current production per unit mass of the electrodynamicstructure (I/M) depends on the electron collection and electron emissiontechnologies and on the weight of the support structures. In oneembodiment, electrodynamic structure 20 includes thin film solar arrays32, thin foil electron collectors 28, FEAC electron emitters 30, and alightweight flexible spin-stabilized structure. In one embodiment,maximum electric current production per unit mass of electrodynamicstructure 20 in LEO is at least 1 Ampere per kilogram (A/kg). It isoverly inefficient for the electrodynamic structure to have maximumelectric current production per unit mass in LEO less than 0.1 A/kg.

In one embodiment, an electrodynamic structure, such as electrodynamicstructure 20, operates without batteries and stores energy in orbitalmotion instead of batteries. In one embodiment, while the electrodynamicstructure is in sunlight, it accumulates energy by gaining altitude.Then, in eclipse, the electrodynamic structure uses the EMF induced insome of its conductors to drive electric currents through otherconductors to produce, for example, out-of-plane forces and to continuechanging the orbit inclination even without direct solar energy input.

In one embodiment, in eclipse, the conductors with largest EMF's can beused for power generation, while other conductors with favorableorientations with respect to the magnetic field can utilize this powerto produce thrust components to change certain orbit elements.

Embodiments of electrodynamic structures having two or three dimensions,such as electrodynamic structure 20, have small dimensions compared toone-dimensional electrodynamic tether systems. Due to these smalldimensions, embodiments of the electrodynamic structures operate withlow voltages that reduce the risk of arcing. In one embodiment,electrodynamic structure 20 has a 400 meter (m) diameter and in LEOexperiences only 80 V or less of EMF induced in its conductors.

Also, embodiments of electrodynamic structures having two or threedimensions, such as electrodynamic structure 20, provide more efficientelectrodynamic propulsion and power generation and can be scaled topropel heavy payloads. In one embodiment, a 900-1000 kg electrodynamicstructure that is 400 m in diameter can change the inclination of a2,000 kg payload in LEO at a rate of up to 0.7 degrees per day. To matchthis performance, an electrodynamic tether would need to be 80 km longand be able to operate at a voltage of 16 kV.

In addition, embodiments of electrodynamic structures having two orthree dimensions, such as electrodynamic structure 20, are inherentlyresistant to meteor and debris damage. This is due at least in part todistributed designs and the redundancy of components. In the case ofdamage to one or more of the electron collectors, electron emitters,solar arrays, and/or supports, the controllers (e.g., controller 34) canreconfigure the conductive paths to bypass the failed component(s) andreroutes currents.

FIG. 3 is a diagram illustrating one embodiment of electrical components60 in a portion of a periphery area, such as periphery area 22. Theelectrical components 60 include electron collectors 28 a-28 c, electronemitters 30 a and 30 b, solar arrays 32 a-32 c, and switches 62 a and 62b. The conductive paths that electrically couple electron collectors 28,electron emitters 30, solar arrays 32, and one or more controllers 34include switches 62 a and 62 b.

Electron collector 28 a is electrically coupled to switch 62 a viaconductive path 64. Electron collector 28 b is electrically coupled toswitch 62 a via conductive path 66 and to switch 62 b via conductivepath 68. Electron collector 28 c is electrically coupled to switch 62 bvia conductive path 70. Solar array 32 a is electrically coupled toswitch 62 a via conductive path 72. Solar array 32 b is electricallycoupled to switch 62 a via conductive path 74 and to switch 62 b viaconductive path 76. Solar array 32 c is electrically coupled to switch62 b via conductive path 78. Electron emitter 30 a is electricallycoupled to switch 62 a via conductive path 80 and electron emitter 30 bis electrically coupled to switch 62 b via conductive path 82. Switch 62a is electrically coupled to switch 62 b via conductive path 84. Switch62 a is electrically coupled to other switches (not shown) viaconductive paths 86 and 88 and switch 62 b is electrically coupled toother switches (not shown) via conductive paths 90 and 92.

One or more controllers 34 control switches 62 a and 62 b and employ thepower from solar arrays 32 a-32 c to drive electrons acrosselectrodynamic structure 20.

If the electrical components 60 are in the area of electron collectionat 50 (shown in FIG. 2), one or more controllers 34 control switches 62a and 62 b to turn on electron collectors 28 a-28 c and turn offelectron emitters 30 a and 30 b. Also, one or more controllers 34control switches 62 a and 62 b to deliver the voltage produced via solararrays 32 a-32 c to drive the electrons across electrodynamic structure20 via conductors 86, 88, 90, and/or 92.

In one embodiment, in the area of electron collection at 50, one or morecontrollers 34 control switches 62 a and 62 b to couple electroncollectors 28 a-28 c together and the combined electrons are driven tothe area of electron emission at 52 (shown in FIG. 2) via conductivepaths 86, 88, 90, and/or 92. In one embodiment, in the area of electroncollection at 50, one or more controllers 34 control switches 62 a and62 b to drive electrons from each of the electron collectors 28 a-28 cindependently to the area of electron emission at 52 via conductivepaths 86, 88, 90, and/or 92.

If the electrical components 60 are in the area of electron emission at52, one or more controllers 34 control switches 62 a and 62 b to turn onelectron emitters 30 a and 30 b and turn off electron collectors 28 a-28c. Also, one or more controllers 34 control switches 62 a and 62 b todeliver the voltage produced via solar arrays 32 a-32 c to drive theelectrons as needed via conductive paths 86, 88, 90, and/or 92.

In one embodiment, in the area of electron emission at 52, one or morecontrollers 34 control switches 62 a and 62 b to couple electronemitters 30 a and 30 b together and drive electrons from the area ofelectron collection at 50 to both electron emitters 30 a and 30 bsubstantially together via conductive paths 86, 88, 90, and/or 92. Inone embodiment, in the area of electron emission at 52, one or morecontrollers 34 control switches 62 a and 62 b to drive electrons toelectron emitters 30 a and 30 b independently from the area of electroncollection at 50 via conductive paths 86, 88, 90, and/or 92.

FIG. 4 is a diagram illustrating one embodiment of an open net-likecollector structure 94 that can be used in any two- or three-dimensionalelectrodynamic structure. Net-like collector structure 94 includescolumn ligaments 96 and row ligaments 98 that intersect at cross points.In one embodiment, at least some of the column ligaments 96 and rowligaments 98 are narrow tapes with bare metallic surfaces. In oneembodiment, at least some of the column ligaments 96 and row ligaments98 are narrow tapes with bare aluminum surfaces. In other embodiments,column ligaments 96 and row ligaments 98 can be any suitable ligamentmaterial.

The open net-like collector structure 94 is more efficient if columnligaments 96 and row ligaments 98 are spaced at distances S that aremany times larger than the width WL of each of the column ligaments 96and row ligaments 98. The net-like collector structure 94 can cover notonly a relatively narrow band around the periphery (e.g., periphery area22) of an electrodynamic structure, such as electrodynamic structure 20,but also much wider areas, including into the interior (e.g., interiorarea 25) of the electrodynamic structure. In one embodiment, the entiresurface of the electrodynamic structure is used for electron collectionvia an open net-like collector structure, such as open net-likecollector structure 94. In one embodiment, at least a portion of columnligaments 96 and/or row ligaments 98 are simultaneously employed ascollectors and conductors of the conductive paths.

FIG. 5 is a diagram illustrating one embodiment of a circular,two-dimensional, planar electrodynamic structure 100 that includes amesh of conductors 102 disposed in an interior area 105. Electrodynamicstructure 100 is configured to generate power and/or propulsion as itorbits a celestial body having a magnetic field. In one aspect,electrodynamic structure 100 is an electrodynamic sail. In one aspect,electrodynamic structure 100 is similar to electrodynamic structure 20,with the exception that electrodynamic structure 100 includes the meshof conductors 102. In other embodiments, electrodynamic structure 100can be part of any suitable system, such as a space station.

Conductive paths in electrodynamic structure 100 include the mesh ofconductors 102. The mesh of conductors 102 includes conductors thatintersect other conductors and switches situated at the cross points ofthe conductors. The switches are controlled to direct currents throughthe mesh of conductors 102 and across electrodynamic structure 100 andto direct currents in current loops in the mesh of conductors 102. Insome embodiments, meshes of conductors (e.g., the mesh of conductors102) include conductors that include insulated strips of aluminum foil.In some embodiments, meshes of conductors (e.g., the mesh of conductors102) include non-conductive supports.

Electrodynamic structure 100 includes the mesh of conductors 102 andperiphery area 104. Electrodynamic structure 100 is coupled to a payload106. Periphery area 104 is situated at the periphery of electrodynamicstructure 100 and has width W. Payload 106 is mechanically coupled tocomponents in periphery area 104 via the mesh of conductors 102.Interior area 105 is defined between an interior edge of periphery area104 and payload 106. In one embodiment, the mesh of conductors 102 ininterior area 105 are not mounted on a substrate and are not coveredwith material. In some embodiments, the mesh of conductors 102 aremounted on a substrate. In one embodiment, the substrate is reflective.In some embodiments, interior area 105 is covered partially orcompletely with a net-like collector structure, such as net-likecollector structure 94.

In the embodiment illustrated in FIG. 5, periphery area 104 includeselectron collectors 108, electron emitters 110, solar arrays 112, andone or more controllers 114. As illustrated, electron collectors 108 andelectron emitters 110 are situated at an outer rim of the periphery area104. As illustrated, solar arrays 112 are situated on an interior rim ofperiphery area 104.

Electron collectors 108, electron emitters 110, solar arrays 112, andcontrollers 114 are electrically coupled via conductive paths formedwith switches and conductors, including the mesh of conductors 102. Inone embodiment, electron collectors 108 are electrically coupled to eachother via the conductive paths. In one embodiment, electron emitters 110are electrically coupled to each other via the conductive paths. In oneembodiment, solar arrays 112 are electrically coupled to each other viathe conductive paths.

The stabilizing mechanical property of the mesh of conductors 102contributes to stabilizing electrodynamic structure 100. In oneembodiment, the mesh of conductors 102 is a non-rigid mesh. In oneembodiment, the mesh of conductors 102 includes mechanically stiffenedsupports and/or mechanically stiffened conductors.

In one embodiment, the mesh of conductors 102 electrically couplespayload 106 to the components in periphery area 104. In one embodiment,payload 106 receives power from electrical components in periphery area104 via the mesh of conductors 102. In one embodiment, payload 106includes one or more controllers that control operation ofelectrodynamic structure 100 via control signals communicated on themesh of conductors.

One or more controllers 114 control operation of electrodynamicstructure 100 via switches in the conductive paths, including switchesin the mesh of conductors 102.

Electron flow for a two-dimensional electrodynamic structure, such aselectrodynamic structure 100, is described above and illustrated in FIG.2. In electrodynamic structure 100 and other electrodynamic structureshaving meshes of conductors, the currents flowing through the conductivepaths, including currents flowing through the mesh of conductors (e.g.,the mesh of conductors 102), interact with the ambient magnetic field toproduce distributed Ampere forces, which can be employed to change theorbit and the orientation of the electrodynamic structure. Also, as themesh of conductors moves through the ambient magnetic field EMF isproduced in the conductors, which can be used to drive electrons to theopposite side of the electrodynamic structure in the direction of theEMF.

In addition, power from the power system (e.g., solar arrays 112) and/orEMF in the conductors can be used to drive closed-loop currents throughselected closed-loop paths in the mesh of conductors (e.g., the mesh ofconductors 102). This does not require electron collection or electronemission. The closed-loop currents interact with the ambient magneticfield to produce distributed Ampere forces and torques to control theattitude dynamics of the electrodynamic structures (e.g., electrodynamicstructure 100). These closed-loop currents through selected closed-looppaths in the mesh of conductors can provide improved control of theattitude dynamics of the electrodynamic structure via the mesh ofconductors.

Conductors in the conductive paths, including meshes of conductors(e.g., the mesh of conductor 102) can operate bi-directionally in thesense that the electrical current can flow either in the direction ofthe EMF induced in the conductor, or in the reverse direction, dependingon the conductor orientation with respect to the magnetic field, missiongoals, available power, and other system parameters. The reverse currentis driven by available power sources, such as solar arrays. If thecurrent is reversed, electron collection and electron emission locationsare reversed. Meshes of conductors operating in this bi-directionalmanner facilitate electron collection and emission occurring at multiplelocations at the same time, to allow better utilization of thrust andpower generation capabilities and to better control dynamics andoptimize orbital maneuvering.

FIG. 6 is a diagram illustrating one embodiment of a hexagonal,two-dimensional, planar electrodynamic structure 150 that includes atriangular mesh of conductors 152 disposed in an interior area 155.Electrodynamic structure 150 is configured to generate power and/orpropulsion as it orbits a celestial body having a magnetic field. In oneaspect, electrodynamic structure 150 is an electrodynamic sail. In oneaspect, electrodynamic structure 150 is similar to electrodynamicstructure 100, with the exceptions that electrodynamic structure 150 ishexagonal and the conductors in the mesh of conductors 152 formtriangular shaped cells. In other embodiments, electrodynamic structure150 can be part of any suitable system, such as a space station.

Conductive paths in electrodynamic structure 150 include the mesh ofconductors 152. The mesh of conductors 152 includes conductors thatintersect other conductors to form triangular shaped cells. Switches aresituated at the cross points of the conductors to direct currentsthrough the mesh of conductors 152 and across electrodynamic structure150 and to direct currents through closed-loop paths in the mesh ofconductors 152. The triangular shaped cells increase the mechanicalstrength and stability of the mesh of conductors 152 and electrodynamicstructure 150. Also, closed-loop currents driven through selectedclosed-loop paths, including triangular shaped cells, in the mesh ofconductors 152 can provide improved control of the attitude dynamics ofelectrodynamic structure 150. In some embodiments, meshes of conductors(e.g., the mesh of conductors 152) include non-conductive supports.

A mesh of conductors, such as the mesh of conductors 152, which includestriangular shaped cells can be used in any suitable electrodynamicstructure having two or three dimensions. Also, the mesh of conductorsthat includes triangular shaped cells can be used in any suitableelectrodynamic structure having any suitable physical shape, includingcircular, elliptical, square, rectangular, or hexagonal.

Electrodynamic structure 150 includes the mesh of conductors 152 andperiphery area 154. Electrodynamic structure 150 is coupled to a payload156. Periphery area 154 is situated at the periphery of electrodynamicstructure 150 and has width W. Payload 156 is mechanically coupled tocomponents in periphery area 154 via the mesh of conductors 152.Interior area 155 is defined between an interior edge of periphery area154 and payload 156.

As illustrated in FIG. 6, periphery area 154 includes electroncollectors 158, electron emitters 160, solar arrays 162, and one or morecontrollers 164. As illustrated, electron collectors 158 and electronemitters 160 are situated at an outer rim of the periphery area 154. Asillustrated, solar arrays 162 are situated on an interior rim ofperiphery area 154.

Electron collectors 158, electron emitters 160, solar arrays 162, andcontrollers 164 are electrically coupled via conductive paths formedwith switches and conductors, including the mesh of conductors 152. Inone embodiment, electron collectors 158 are electrically coupled to eachother via the conductive paths. In one embodiment, electron emitters 160are electrically coupled to each other via the conductive paths. In oneembodiment, solar arrays 162 are electrically coupled to each other viathe conductive paths.

The stabilizing mechanical property of the mesh of conductors 152contributes to stabilizing electrodynamic structure 150. In addition,the triangular shaped cells formed via the conductors of the mesh ofconductors 152 improve the mechanical strength and stability ofelectrodynamic structure 150. In one embodiment, the mesh of conductors152 is a non-rigid mesh. In one embodiment, the mesh of conductors 152includes mechanically stiffened supports and/or mechanically stiffenedconductors.

In one embodiment, the mesh of conductors 152 electrically couplespayload 156 to electrical components in periphery area 154. In oneembodiment, payload 156 via the mesh of conductors 152 and payload 156receives power from electrical components in periphery area 154 via themesh of conductors 152. In one embodiment, periphery area 154 iselectrically coupled to payload 156 via the mesh of conductors 152 andpayload 156 includes one or more controllers that control operation ofelectrodynamic structure 150 via control signals communicated on themesh of conductors.

One or more controllers 164 control operation of electrodynamicstructure 150 via switches in the conductive paths, including switchesin the mesh of conductors 152.

FIG. 7 is a diagram illustrating one embodiment of a rectangular,two-dimensional, planar electrodynamic structure 200 that includes amesh of conductors 202 disposed in an interior area 205. Electrodynamicstructure 200 is configured to generate power and/or propulsion as itorbits a celestial body having a magnetic field. In one aspect,electrodynamic structure 200 is an electrodynamic sail. In one aspect,electrodynamic structure 200 is similar to electrodynamic structures 100and 150, with the exception that electrodynamic structure 200 isrectangular and the conductors in the mesh of conductors 202 formrectangular shaped cells. In other embodiments, electrodynamic structure200 can be part of any suitable system, such as a space station. In oneembodiment, electrodynamic structure 200 is square.

Conductive paths in electrodynamic structure 200 include the mesh ofconductors 202. The mesh of conductors 202 includes conductors thatintersect other conductors to form rectangular shaped cells. Switchesare situated at the cross points of the conductors to direct currentsthrough the mesh of conductors 202 and across electrodynamic structure200 and to direct currents through closed-loop paths in the mesh ofconductors 202. The mesh of conductors 202 increases the mechanicalstrength and stability of electrodynamic structure 200. Also,closed-loop currents driven through selected closed-loop paths in themesh of conductors 202 can provide improved control of the attitudedynamics of electrodynamic structure 200. In some embodiments, meshes ofconductors (e.g., the mesh of conductors 202) include non-conductivesupports.

Electrodynamic structure 200 includes the mesh of conductors 202 andperiphery area 204. Electrodynamic structure 200 is coupled to a payload206. Periphery area 204 is situated at the periphery of electrodynamicstructure 200 and has width W. Payload 206 is mechanically coupled tocomponents in periphery area 204 via the mesh of conductors 202.Interior area 205 is defined between an interior edge of periphery area204 and payload 206.

As illustrated in FIG. 7, periphery area 204 includes electroncollectors 208, electron emitters 210, solar arrays 212, and one or morecontrollers 214. As illustrated, electron collectors 208 and electronemitters 210 are situated at an outer rim of the periphery area 204. Asillustrated, solar arrays 212 are situated on an interior rim ofperiphery area 204.

Electron collectors 208, electron emitters 210, solar arrays 212, andcontroller 214 are electrically coupled via conductive paths formed withswitches and conductors, including the mesh of conductors 202. In oneembodiment, electron collectors 208 are electrically coupled to eachother via the conductive paths. In one embodiment, electron emitters 210are electrically coupled to each other via the conductive paths. In oneembodiment, solar arrays 212 are electrically coupled to each other viathe conductive paths.

The stabilizing mechanical property of the mesh of conductors 202contributes to stabilizing electrodynamic structure 200. In oneembodiment, the mesh of conductors 202 is a non-rigid mesh. In oneembodiment, the mesh of conductors 202 includes mechanically stiffenedsupports and/or mechanically stiffened conductors.

In one embodiment, the mesh of conductors 202 electrically couplespayload 206 to electrical components in periphery area 204. In oneembodiment, payload 206 receives power from electrical components inperiphery area 204 via the mesh of conductors 202. In one embodiment,payload 206 includes one or more controllers that control operation ofelectrodynamic structure 200 via control signals communicated on themesh of conductors.

One or more controllers 214 control operation of electrodynamicstructure 200 via the switches in the conductive paths, including theswitches in the mesh of conductors 202.

FIG. 8 is a diagram illustrating one embodiment of a rectangular,two-dimensional, planar electrodynamic structure 250 that has peripheryutilization for electron collection and electron emission U of lessthan 1. In one embodiment, electrodynamic structure 250 has peripheryutilization for electron collection and electron emission Usubstantially equal to ½. In other embodiments, electrodynamic structure250 is an elongated rectangle and the periphery utilization for electroncollection and electron emission U is less than ½.

Electrodynamic structure 250 is configured to generate power and/orpropulsion as it orbits a celestial body having a magnetic field. In oneaspect, electrodynamic structure 250 is an electrodynamic sail. In oneaspect, electrodynamic structure 250 is similar to electrodynamicstructure 200, with the exception that electrodynamic structure 250 doesnot have electron collectors or electron emitters on the top and bottom,such that periphery utilization U has been reduced to less than 1. Inother embodiments, electrodynamic structure 250 can be part of anysuitable system, such as a space station.

Electrodynamic structure 250 includes a mesh of conductors 252, a firstperiphery area 254 a, and a second periphery area 254 b. Electrodynamicstructure 250 is coupled to a payload 256. First periphery area 254 a issituated at one side periphery of electrodynamic structure 250 and haswidth W. Second periphery area 254 b is situated at the other sideperiphery of electrodynamic structure 250 and has width W. The mesh ofconductors 252 are disposed in an interior area 255 defined by interioredges of periphery areas 254 a and 254 b and interior edges of the topand bottom periphery of electrodynamic structure 250. Interior area 255is defined between these defining interior edges and payload 256.Payload 256 is mechanically coupled to components in periphery areas 254a and 254 b via the mesh of conductors 252. In some embodiments, meshesof conductors (e.g., the mesh of conductors 252) include non-conductivesupports.

As illustrated in FIG. 8, first periphery area 254 a includes electroncollectors 258 a, electron emitters 260 a, solar arrays 262 a, and oneor more controllers 264. Electron collectors 258 a and electron emitters260 a are situated at an outer rim of first periphery area 254 a. Solararrays 262 a are situated on an interior rim of first periphery area 254a.

As illustrated in FIG. 8, second periphery area 254 b includes electroncollectors 258 b, electron emitters 260 b, and solar arrays 262 b.Second periphery area 254 b can also include one or more controllers264. Electron collectors 258 b and electron emitters 260 b are situatedat an outer rim of second periphery area 254 b. Solar arrays 262 b aresituated on an interior rim of second periphery area 254 b.

Electron collectors 258, electron emitters 260, solar arrays 262, andcontrollers 264 are electrically coupled via conductive paths formedwith switches and conductors, including the mesh of conductors 252. Inone embodiment, electron collectors 258 a are electrically coupled toeach other via the conductive paths. In one embodiment, electroncollectors 258 b are electrically coupled to each other via theconductive paths. In one embodiment, electron emitters 260 a areelectrically coupled to each other via the conductive paths. In oneembodiment, electron emitters 260 b are electrically coupled to eachother via the conductive paths. In one embodiment, solar arrays 262 aare electrically coupled to each other via the conductive paths. In oneembodiment, solar arrays 262 b are electrically coupled to each othervia the conductive paths.

The stabilizing mechanical property of the mesh of conductors 252contributes to stabilizing electrodynamic structure 250. In oneembodiment, the mesh of conductors 252 is a non-rigid mesh. In oneembodiment, the mesh of conductors 252 includes mechanically stiffenedsupports and/or mechanically stiffened conductors. In some embodiments,meshes of conductors (e.g., the mesh of conductors 252) includenon-conductive supports.

Conductive paths in electrodynamic structure 250 include the mesh ofconductors 252. The mesh of conductors 252 includes conductors thatintersect other conductors to form rectangular shaped cells. Switchesare situated at the cross points of the conductors to direct currentsthrough the mesh of conductors 252 and across electrodynamic structure250 and to direct currents through closed-loop paths in the mesh ofconductors 252. Closed-loop currents driven through selected closed-looppaths in the mesh of conductors 252 provide improved control of theattitude dynamics of electrodynamic structure 250.

In one embodiment, the mesh of conductors 252 electrically couplespayload 256 to electrical components in first periphery area 254 aand/or second periphery area 254 b. In one embodiment, payload 256receives power from electrical components in the first periphery area254 a and/or second periphery area 254 b via the mesh of conductors 252.In one embodiment, payload 256 includes one or more controllers thatcontrol operation of electrodynamic structure 250 via control signalscommunicated on the mesh of conductors.

One or more controllers 264 control operation of electrodynamicstructure 250 via the switches in the conductive paths, includingswitches in the mesh of conductors 252.

The performance level of electrodynamic structure 250 can be estimatedvia Equation I. For a periphery utilization of U=1, the entire peripheryof the electrodynamic structure is lined with electron collectors andelectron emitters, such as with the rectangular electrodynamic structure200 illustrated in FIG. 7. Electrodynamic structure 250, however, doesnot have electron collectors or electron emitters on the top and bottomsides. Thus, electrodynamic structure 250 has a periphery utilizationfor electron collection and electron emission U of less than 1. In oneembodiment, electrodynamic structure 250 is substantially square and theperiphery utilization for electron collection and electron emission U issubstantially equal to ½. In other embodiments, electrodynamic structure250 is an elongated rectangle having longer top and bottom sides and theperiphery utilization for electron collection and electron emission U isless than ½. It is overly inefficient for the electrodynamic structureto have periphery utilization U of less than ⅕.

The area to perimeter parameter (S/P) is maximized if the electrodynamicstructure is circular. If electrodynamic structure 250 is square, thearea to perimeter ratio (S/P) is slightly smaller. Also, ifelectrodynamic structure 250 is rectangular, the area to perimeter ratio(S/P) is lower. It is overly inefficient for the electrodynamicstructure to have an area to perimeter ratio (S/P) of less than ¼ of theratio for a circle with the same perimeter.

FIG. 9 is a diagram illustrating one embodiment of a cylindrical,three-dimensional electrodynamic structure 300 that is configured togenerate power and/or propulsion as it orbits a celestial body having amagnetic field. In one aspect, electrodynamic structure 300 is anelectrodynamic sail. In one aspect, electrodynamic structure 300 issimilar to circular, two-dimensional electrodynamic structure 20, withthe exception that electrodynamic structure 300 includes one or moreperiphery areas situated at the periphery of electrodynamic structure300 and perpendicular to the plane of electrodynamic structure 300. Inother embodiments, electrodynamic structure 300 can be part of anysuitable system, such as a space station.

Electrodynamic structure 300 includes supports 302 and periphery areawith sections 304 a-304 d. Electrodynamic structure 300 is coupled to apayload 306. The sections of the periphery area 304 a-304 d are situatednext to each other at the periphery of electrodynamic structure 300 andperpendicular to the plane of supports 302. Payload 306 is mechanicallycoupled to components in one or more periphery area sections 304 a-304 dvia supports 302. An interior area 305 is defined between at least oneinterior edge of at least one of periphery area sections 304 a-304 d andpayload 306. In some embodiments, periphery area sections have stiffnesselements to maintain their shape and orientation.

In one embodiment, each of the periphery area sections 304 a-304 dincludes electron collectors, electron emitters, and solar arrays, whichare suitably arranged and electrically coupled via conductive pathsformed with switches and conductors (not shown for clarity). In someembodiments, electron collectors and/or solar arrays are suitablyarranged and electrically coupled in interior area 305. In someembodiments, the electron collectors, electron emitters, and solararrays are electrically coupled via conductive paths including a mesh ofconductors.

In one embodiment, supports 302 are non-rigid supports. In oneembodiment, supports 302 include mechanically stiffened supports and/ormechanically stiffened conductors. In one embodiment, one or more of thesupports 302 electrically couple payload 306 to electrical components inone or more periphery areas 304 a-304 d. In one embodiment,electrodynamic structure 300 includes a mesh of conductors in place ofsupports 302 to mechanically and electrically couple payload 306 tocomponents in one or more periphery area sections 304 a-304 d.

In one embodiment, payload 306 receives power from electrical componentsin one or more periphery area sections 304 a-304 d via conductive paths.In one embodiment, payload 306 includes one or more controllers thatcontrol operation of electrodynamic structure 300.

Electrodynamic structure 300 includes one or more controllers thatcontrols operation of electrodynamic structure 300 via the switches inthe conductive paths. The one or more controllers control electroncollectors on one side of electrodynamic structure 300 to collectelectrons from the ambient plasma and electron emitters on the oppositeside of electrodynamic structure 300 to emit the electrons into theambient plasma. Also, the controller controls power generation via apower system (e.g., solar arrays) and/or EMF in the conductors to drivethe collected electrons to the electron emitters on the opposite side ofelectrodynamic structure 300.

Similar to as described above for two-dimensional electrodynamicstructures, in three-dimensional electrodynamic structures (e.g.,electrodynamic structure 300), the currents flowing through theconductive paths interact with the ambient magnetic field to producedistributed Ampere forces. These forces can be used to change the orbitand the orientation of the three-dimensional electrodynamic structure.Also, the motion through the ambient magnetic field produces EMF in theconductors, which can be used to drive electrons to the opposite side ofthe three-dimensional electrodynamic structure.

Electrodynamic structure 300 is substantially a three-dimensionalelectrodynamic structure that has a two-dimensional projection 308 fromthe periphery of the three-dimensional structure. Periphery areasections 304 a-304 d project to a corresponding two-dimensionalprojected periphery area 310. Interior area 305 projects to acorresponding two-dimensional projected interior area 312.

If electrodynamic structure 300 is spin stabilized with the spin axisnormal to the plane of supports 302, spin characteristics and dynamicsof electrodynamic structure 300 are similar to spin characteristics anddynamics described above for two-dimensional electrodynamic structures.

The performance level of electrodynamic structure 300 can be estimatedvia Equation I as applied to electrodynamic structure 300 and thetwo-dimensional projection 308.

In some embodiments, all periphery area sections 304 a-304 d includeelectron collectors and electron emitters on the entire periphery ofelectrodynamic structure 300, which yields a utilization factor of U=1.If half of the periphery of the electrodynamic structure 300 includeselectron collectors and electron emitters and the other half is empty,U=½.

The area to perimeter ratio (S/P) is calculated from the two-dimensionalprojection at 308. The periphery of the three-dimensional structure 300defines the perimeter of the two-dimensional projection 308. Thetwo-dimensional projection at 308 is circular, which provides the bestarea to perimeter ratio (S/P). Other shapes, such as square or hexagonalshapes, provide smaller area to perimeter ratios (S/P). Elongatedshapes, such as elongated elliptical shapes and elongated rectangularshapes have even lower area to perimeter ratios (S/P).

The electric current production per unit mass of the electrodynamicstructure (I/M) depends on the electron collection and electron emissiontechnologies and on the weight of the support structures. In oneembodiment, electrodynamic structure 300 has a lower specific currentproduction rate I/M due to the mass of additional support structures,such as stiffness elements, used to maintain the non-planar shape.

FIG. 10 is a diagram illustrating one embodiment of a curved,half-elliptical, three-dimensional electrodynamic structure 400 that isconfigured to generate power and/or propulsion as it orbits a celestialbody having a magnetic field. In one aspect, electrodynamic structure400 is an electrodynamic sail. In one aspect, electrodynamic structure400 is similar to two-dimensional electrodynamic structure 100, with theexception that electrodynamic structure 400 is a curved, ellipticalshape and includes multiple sections of the periphery area 404 a and 404b. In other embodiments, electrodynamic structure 400 can be part of anysuitable system, such as a space station.

Electrodynamic structure 400 includes a mesh of conductors 402 andperiphery area sections 404 a and 404 b. Electrodynamic structure 400 iscoupled to a payload 406. Periphery area sections 404 a and 404 b aresituated next to each other at the periphery of electrodynamic structure400. Payload 406 is mechanically coupled to components in one or moreperiphery area sections 404 a and 404 b via the mesh of conductors 402.An interior area 405 is defined between an interior edge of peripheryarea section 404 b and payload 406. The mesh of conductors 402 aredisposed in interior area 405. In some embodiments, meshes of conductors(e.g., the mesh of conductors 402) include non-conductive supports.

In one embodiment, each of the periphery area sections 404 a and 404 bincludes electron collectors, electron emitters, and solar arrays, whichare suitably arranged and electrically coupled via conductive pathsformed with switches and conductors, including the mesh of conductors402. In some embodiments, electron collectors and/or solar arrays aresuitably arranged and electrically coupled in interior area 405.

The stabilizing mechanical property of the mesh of conductors 402contributes to stabilizing electrodynamic structure 400. In oneembodiment, the mesh of conductors 402 is a non-rigid mesh. In oneembodiment, the mesh of conductors 402 includes mechanically stiffenedsupports and/or mechanically stiffened conductors.

Conductive paths in electrodynamic structure 400 include the mesh ofconductors 402. The mesh of conductors 402 includes conductors thatintersect other conductors and switches situated at the cross points ofthe conductors. The switches are controlled to direct currents throughthe mesh of conductors 402 and across electrodynamic structure 400 andto direct currents in current loops in the mesh of conductors 402.

In one embodiment, the mesh of conductors 402 electrically couplespayload 406 to the electrical components in one or more periphery areasections 404. In one embodiment, payload 406 receives power fromelectrical components in one or more periphery area sections 404 via themesh of conductors 402. In one embodiment, payload 406 includes one ormore controllers that control operation of electrodynamic structure 400via control signals communicated on the mesh of conductors 402.

Electrodynamic structure 400 includes one or more controller thatcontrols operation of electrodynamic structure 400 via switches in theconductive paths, including switches in the mesh of conductors 402.

Electrodynamic structure 400 is substantially a three-dimensionalelectrodynamic structure that has a two-dimensional projection 408 fromthe periphery of the three-dimensional structure. Periphery areasections 404 a and 404 b project to a corresponding two-dimensionalprojected periphery area 410. Interior area 405 projects to acorresponding two-dimensional projected interior area 412.

If electrodynamic structure 400 is spin stabilized with the spin axisnormal to the plane of projection 408, spin characteristics and dynamicsof electrodynamic structure 400 are similar to spin characteristics anddynamics described above for two-dimensional electrodynamic structures.In addition, similar to as described above for two-dimensionalelectrodynamic structures having meshes of conductors closed-loopcurrents through selected closed-loop paths in the mesh of conductors402 can provide improved control of the attitude dynamics ofelectrodynamic structure 400 via the mesh of conductors 402.

The performance level of electrodynamic structure 400 can be estimatedvia Equation I as applied to electrodynamic structure 400 and thetwo-dimensional projection 408.

In some embodiments, both periphery area sections 404 a and 404 binclude electron collectors and electron emitters on the entireperiphery of electrodynamic structure 400, which yields a utilizationfactor of U=1. If half of the periphery of the electrodynamic structure400 includes electron collectors and electron emitters and the otherhalf is empty, U=½.

The area to perimeter ratio (S/P) is calculated from the two-dimensionalprojection at 408. The periphery of the three-dimensional structure 400defines the perimeter of the two-dimensional projection 408. Thetwo-dimensional projection at 408 is circular, which provides the bestarea to perimeter ratio (S/P). Other shapes, such as square or hexagonalshapes, provide smaller area to perimeter ratios (S/P). Elongatedshapes, such as elongated elliptical shapes and elongated rectangularshapes have even lower area to perimeter ratios (S/P).

The electric current production per unit mass of the electrodynamicstructure (I/M) depends on the electron collection and electron emissiontechnologies and on the weight of the support structures. In oneembodiment, electrodynamic structure 400 has a lower specific currentproduction rate I/M due to the mass of additional support structures,such as stiffness elements, used to maintain the non-planar shape.

FIG. 11 is a diagram illustrating one embodiment of an enclosed,three-dimensional electrodynamic structure 500 that includes an upperconical section 502 and a lower conical section 504 coupled at a line ofconnection 506. Periphery area 508 a is situated at the periphery ofupper conical section 502. Periphery area 508 b is situated at theperiphery of lower conical section 504. Periphery areas 508 a and 508 bmeet at the line of connection 506.

Electrodynamic structure 500 is configured to generate power and/orpropulsion as it orbits a celestial body having a magnetic field. In oneaspect, electrodynamic structure 500 is an electrodynamic sail. In otherembodiments, electrodynamic structure 500 can be part of any suitablesystem, such as a space station.

Electrodynamic structure 500 includes periphery areas 508 a and 508 b,an upper mesh of conductors 510, and a lower mesh of conductors 512.Electrodynamic structure 500 can be coupled to a payload situated insideelectrodynamic structure 500 or at a point of one of the conicalsections 502 and 504. The payload can be mechanically coupled to theupper mesh of conductors 510 and/or the lower mesh of conductors 512. Inone embodiment, components in periphery areas 508 a and 508 b arecoupled to each other at the line of connection 506. The upper mesh ofconductors 510 and the lower mesh of conductors 512 arethree-dimensional meshes. In one embodiment, the upper mesh ofconductors 510 and the lower mesh of conductors 512 are not mounted on asubstrate and are not covered with material. In some embodiments, theupper mesh of conductors 510 and the lower mesh of conductors 512 aremounted on a substrate. In one embodiment, the substrate is reflective.In some embodiments, meshes of conductors (e.g., the mesh of conductors510) include non-conductive supports.

In one embodiment, each of the periphery areas 508 a and 508 b includeselectron collectors, electron emitters, and solar arrays, which aresuitably arranged and electrically coupled via conductive paths formedwith switches and conductors, which include the upper and lower meshesof conductors 510 and 512. In some embodiments, electron collectorsand/or solar arrays are suitably arranged and electrically coupled onsurfaces of conical sections 502 and 504 other than in the peripheryareas 508 a and 508 b.

The stabilizing mechanical properties of the upper and lower meshes ofconductors 510 and 512 contribute to stabilizing electrodynamicstructure 500. In one embodiment, each of the upper and lower meshes ofconductors 510 and 512 is a non-rigid mesh. In one embodiment, each ofthe upper and lower meshes of conductors 510 and 512 includesmechanically stiffened supports and/or mechanically stiffenedconductors. In one embodiment, electrodynamic structure 500 includesstiffness supports between conical sections 502 and 504 to maintain itsnon-planar shape.

Conductive paths in electrodynamic structure 500 include the upper andlower meshes of conductors 510 and 512. Each of the upper and lowermeshes of conductors 510 and 512 includes conductors that intersectother conductors and switches situated at the cross points of theconductors. The switches are controlled to direct currents through theupper and lower meshes of conductors 510 and 512 and acrosselectrodynamic structure 500 and to direct currents in current loops ineach of the upper and lower meshes of conductors 510 and 512.

In one embodiment, one or more of the upper and lower meshes ofconductors 510 and 512 electrically couples the payload to electricalcomponents in one or more periphery areas 508 a and 508 b. In oneembodiment, the payload receives power from electrical components in oneor more periphery areas 508 a and 508 b via one or both of the upper andlower meshes of conductors 510 and 512. In one embodiment, the payloadincludes one or more controllers that control operation ofelectrodynamic structure 500 via control signals communicated on one orboth of the mesh of conductors 510 and 512.

Electrodynamic structure 500 includes one or more controllers thatcontrol operation of electrodynamic structure 500 via switches in theconductive paths, including switches in the upper and lower meshes ofconductors 510 and 512.

Electrodynamic structure 500 is substantially a three-dimensionalelectrodynamic structure that has a two-dimensional projection 514 fromthe periphery of the three-dimensional structure. Periphery areas 508 aand 508 b project to a two-dimensional projected periphery area 516. Theportions of conical sections 502 and 504 that do not include peripheryareas 508 a and 508 b project to a corresponding two-dimensionalprojected interior area 518.

If electrodynamic structure 500 is spin stabilized with the spin axisnormal to the plane of projection 514, spin characteristics and dynamicsof electrodynamic structure 500 are similar to spin characteristics anddynamics described above for two-dimensional electrodynamic structures.In addition, similar to as described above for two-dimensionalelectrodynamic structures having meshes of conductors closed-loopcurrents through selected closed-loop paths in the upper and lowermeshes of conductors 510 and 512 can provide improved control of theattitude dynamics of electrodynamic structure 500.

The performance level of electrodynamic structure 500 can be estimatedvia Equation I as applied to electrodynamic structure 500 and thetwo-dimensional projection 514.

In some embodiments, both periphery areas 508 a and 508 b includeelectron collectors and electron emitters on the entire periphery ofelectrodynamic structure 500, which yields a utilization factor of U=1.If half of the periphery of the electrodynamic structure 500 includeselectron collectors and electron emitters and the other half is empty,U=½.

The area to perimeter ratio (S/P) is calculated from the two-dimensionalprojection at 514. The periphery of the three-dimensional structure 500defines the perimeter of the two-dimensional projection 514. Thetwo-dimensional projection at 514 is circular, which provides the bestarea to perimeter ratio (S/P). Other shapes, such as square or hexagonalshapes, provide smaller area to perimeter ratios (S/P). Elongatedshapes, such as elongated elliptical shapes and elongated rectangularshapes have even lower area to perimeter ratio (S/P).

The electric current production per unit mass of the electrodynamicstructure (I/M) depends on the electron collection and electron emissiontechnologies and on the weight of the support structures. In oneembodiment, electrodynamic structure 500 has a lower specific currentproduction rate I/M due to the mass of additional support structures,such as stiffness elements, used to maintain the non-planar shape.

Two- and three-dimensional electrodynamic structures can fly a varietyof missions, taking advantage of propellantless propulsion and virtuallyunlimited changes in velocity. Two- and three-dimensional electrodynamicstructures can repeatedly go from orbit to orbit, with or withoutpayloads, dramatically changing orbital elements in a matter of weeks ormonths, and keeping all inclinations within reach.

If desired, the propulsion capabilities of the two- andthree-dimensional electrodynamic structures can be augmented by mountingion thrusters at various points of the electrodynamic structure andutilizing some of the energy collected by the solar arrays of theelectrodynamic structure for ion propulsion.

Although specific embodiments have been illustrated and describedherein, it will be appreciated by those of ordinary skill in the artthat a variety of alternate and/or equivalent implementations may besubstituted for the specific embodiments shown and described withoutdeparting from the scope of the present invention. This application isintended to cover any adaptations or variations of the specificembodiments discussed herein. Therefore, it is intended that thisinvention be limited only by the claims and the equivalents thereof.

1. An electrodynamic method comprising: providing an electrodynamicstructure with a periphery; providing power; collecting electrons withcollectors; emitting electrons with emitters; and conducting currentthrough conductive paths to provide at least one of electrodynamicpropulsion and power generation; wherein the emitting electrons and thecollecting electrons utilizes at least 20% of the periphery of theelectrodynamic structure adjacent to the perimeter of the largest planarprojection area of the smallest single shape without holes enclosing thecollectors, the emitters, and the conductive paths.
 2. Theelectrodynamic method of claim 1, comprising: controlling collectingelectrons, emitting electrons, and conducting current to provide the atleast one of electrodynamic propulsion and power generation.
 3. Theelectrodynamic method of claim 1, comprising: controlling collectingelectrons, emitting electrons, and conducting to control system dynamicsthrough an interaction between electric currents and an ambient magneticfield.
 4. The electrodynamic method of claim 1, comprising: controllingswitches in the conductive paths to direct current through theconductive paths and provide the at least one of electrodynamicpropulsion and power generation.
 5. The electrodynamic method of claim1, wherein the largest planar projection area of the smallest singleshape without holes enclosing the collectors, the emitters, and theconductive paths is at least 25% of an area of a circle having a circleperimeter equal to the perimeter of the largest planar projection area.6. The electrodynamic method of claim 1, comprising: changing directionof the conducting current to control the at least one of electrodynamicpropulsion and power generation.
 7. The electrodynamic method of claim1, comprising: controlling collecting electrons, emitting electrons, andconducting current to generate power from electro-motive force.
 8. Theelectrodynamic method of claim 1, comprising: controlling collectingelectrons, emitting electrons, and conducting current to control solarenergy collection rates.
 9. The electrodynamic method of claim 1,comprising: controlling collecting electrons, emitting electrons, andconducting current to produce a cumulative variation of orbital elementsover a given period of time.
 10. The electrodynamic method of claim 1,comprising: controlling collecting electrons, emitting electrons, andconducting current to change at least one of spin axis, spin phase, androtation rate.
 11. The electrodynamic method of claim 1, comprising:controlling switches in the conductive paths to control closed loopcurrents and produce torque to thereby control an attitude of theelectrodynamic structure.
 12. The electrodynamic method of claim 1,comprising: controlling conducting current to control rotation rate ofthe electrodynamic structure to spin stabilize the electrodynamicstructure.
 13. The electrodynamic method of claim 1, comprising:providing a total length of conductors at least 20% larger than theperimeter of the largest planar projection area of the smallest singleshape without holes enclosing the collectors, the emitters, and theconductive paths.
 14. An electrodynamic method comprising: providing anelectrodynamic structure; providing power; collecting electrons withcollectors; emitting electrons with emitters; providing a total lengthof conductors at least 20% larger than the perimeter of the largestplanar projection area of the smallest single shape without holesenclosing the collectors, the emitters, and the conductors; andconducting current through the conductors to provide at least one ofelectrodynamic propulsion and power generation.
 15. The electrodynamicmethod of claim 14, comprising: controlling collecting electrons,emitting electrons, and conducting current to provide the at least oneof electrodynamic propulsion and power generation.
 16. Theelectrodynamic method of claim 14, comprising: controlling collectingelectrons, emitting electrons, and conducting to control system dynamicsthrough an interaction between electric currents and an ambient magneticfield.
 17. The electrodynamic method of claim 14, comprising:controlling switches to direct current through the conductors andprovide the at least one of electrodynamic propulsion and powergeneration.
 18. The electrodynamic method of claim 14, wherein thelargest planar projection area of the smallest single shape withoutholes enclosing the collectors, the emitters, and the conductors is atleast 25% of an area of a circle having a circle perimeter equal to theperimeter of the largest planar projection area.
 19. The electrodynamicmethod of claim 14, comprising: changing direction of the conductingcurrent to control the at least one of electrodynamic propulsion andpower generation.
 20. The electrodynamic method of claim 14, comprising:controlling collecting electrons, emitting electrons, and conductingcurrent to generate power from electro-motive force.
 21. Theelectrodynamic method of claim 14, comprising: controlling collectingelectrons, emitting electrons, and conducting current to control solarenergy collection rates.
 22. The electrodynamic method of claim 14,comprising: controlling collecting electrons, emitting electrons, andconducting current to produce a cumulative variation of orbital elementsover a given period of time.
 23. The electrodynamic method of claim 14,comprising: controlling collecting electrons, emitting electrons, andconducting current to change at least one of spin axis, spin phase, androtation rate.
 24. The electrodynamic method of claim 14, comprising:controlling switches to control closed loop currents and produce torqueto thereby control an attitude of the electrodynamic structure.
 25. Theelectrodynamic method of claim 14, comprising: controlling conductingcurrent to control rotation rate of the electrodynamic structure to spinstabilize the electrodynamic structure.
 26. The electrodynamic method ofclaim 14, wherein the electrodynamic structure has a periphery and theemitting electrons and the collecting electrons utilizes at least 20% ofthe periphery of the electrodynamic structure.
 27. An electrodynamicmethod comprising: providing an electrodynamic structure with aperiphery; providing power; collecting electrons with collectors;emitting electrons with emitters, wherein the emitting electrons and thecollecting electrons utilizes at least 20% of the periphery of theelectrodynamic structure; and conducting current through conductivepaths to provide at least one of electrodynamic propulsion and powergeneration; wherein the largest planar projection area of the smallestsingle shape without holes enclosing the collectors, the emitters, andthe conductive paths is at least 25% of an area of a circle having acircle perimeter equal to the perimeter of the largest planar projectionarea.